Erika, Xylia and Gem had 1404 pens. Xylia won some of the pens from Erika and as a result, Xylia's pens increased by 50%. Gem then won some pens from Xylia and Gem's pens increased by 30%. Finally, Gem lost some of her pens to Erika and Erika's pens increased by 20%. In the end, they realised that they each had an equal number of pens. How many percent less did Erika have in the end than what she had at first? Correct your answer to 1 decimal place.

Erika	Xylia	Gem
1404
	2 u
- 1 u	+ 1 u
	3 u
		10 p
	- 3 p	+ 3 p
		13 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
30% = ³⁰₁₀₀ = ³₁₀
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 1404

1 group = 1404 ÷ 3 = 468

1 group = 6 boxes
6 boxes = 468

1 box = 468 ÷ 6 = 78

1 group + 1 box = 13 p
468 + 78 = 13 p
13 p = 546

1 p = 546 ÷ 13 = 42

3 p = 3 x 42 = 126

1 group + 3 p = 3 u
468 + 126 = 3 u
3 u = 594

1 u = 594 ÷ 3 = 198

Number of pens that Erika had at first
= 5 boxes + 1 u
= (5 x 78) + 198
= 390 + 198
= 588

Percent that Erika had less in the end than at first
= ^{588 - 468}₅₈₈ x 100%
≈ 20.4%

Answer(s): 20.4%